Snub cube

The snub cube or snub cuboctahedron is an Archimedean solid, usually regarded as a truncated polyhedron derived by truncating either a cube or an octahedron.

Canonical coordinates for a snub cube are all the even permutations of (±1, ±ξ, ±1/ξ) with an even number of plusses, along with all the odd permutations with an odd number of plusses, where ξ is the real solution to ξ³+ξ²+ξ=1, which is (³√(17+√297)+³√(17-√297)-1)/3. Taking the even permutations with an odd number of plusses, and the odd permutations with an even number of plusses gives a different snub cube, a mirror image.

The snub cube has 38 faces, of which 6 are squares and the other 32 are equilateral triangles. It also has 60 edges, and 24 vertices. In three-dimensional space, it has two distinct forms, which are mirror images (or "enantiomorphs") of each other. In higher-dimensional spaces, these are congruent.

The snub cube should not be confused with the truncated cube.